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# Untitled

a guest Jul 20th, 2019 66 Never
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1. (*Initial Parameters*)Needs["NDSolve`FEM`"];
2. Mobi = 1.0; lame = 0.01; noise = 0.02; conu0 = 0.63;
3. xmax = 1.0;
4. ymax = 1.0;
5. tmax = 1.0;
6.
7. [CapitalOmega] = Rectangle[{0, 0}, {a, b}] /. {a -> 1, b -> 1};
8. RegionPlot[[CapitalOmega], AspectRatio -> Automatic]
9. mesh = ToElementMesh[[CapitalOmega], "MaxCellMeasure" -> 1/1000,
11. mesh["Wireframe"]
12. n = Length[mesh["Coordinates"]]
13. u0 = ElementMeshInterpolation[{mesh},
14.    conu0 + noise*(0.5 - RandomReal[{0, 1}, n])];
15. Plot3D[u0[x, y], {x, y} [Element] mesh]
16.
17. op1 = !(
18. *SubscriptBox[([PartialD]), (t)](u[t, x, y])) - !(
19. *SubsuperscriptBox[([Del]), ({x, y}), (2)](v[t, x, y]))*
20.    Mobi
21.
22. op2 = v[t, x, y] -
23.   200 *u[t, x, y] (1 - 3 *u[t, x, y] + 2 *u[t, x, y]^2) + lame*!(
24. *SubsuperscriptBox[([Del]), ({x, y}), (2)](u[t, x, y]))
25.
26. {unn, vnn} =
27.   NDSolve[{op1 == 0, op2 == 0, u[0, x, y] == u0[x, y],
28.     v[0, x, y] == 0}, {u, v}, {t, 0, tmax}, {x, y} [Element] mesh];
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